17 (seventeen) is the natural number In mathematics, there are two conventions for the set of natural numbers: it is either the set of positive integers {1, 2, 3, ...} according to the traditional definition; or the set of non-negative integers {0, 1, 2, ...} according to a definition first appearing in the nineteenth century following 16 and preceding 18. It is prime In mathematics, a prime number is a natural number that has exactly two distinct natural number divisors: 1 and itself. The smallest twenty-five prime numbers (all the prime numbers under 100) are:.

In speech, the numbers 17 and 70 are often confused as they sound similar. When carefully enunciated, they differ in which syllable is stressed In linguistics, stress is the relative emphasis that may be given to certain syllables in a word, or to certain words in a phrase or sentence. The term is also used for similar patterns of phonetic prominence inside syllables. The word accent is sometimes also used with this sense: 17 /sɛvɨnˈtiːn/ vs 70 /ˈsɛvɨnti/. However, in dates such as 1789 Year 1789 was a common year starting on Thursday (link will display the full calendar) of the Gregorian calendar (or a common year starting on Monday of the 11-day slower Julian calendar) or when contrasting numbers in the teens, such as 16, 17, 18, the stress shifts to the first syllable: 17 /ˈsɛvɨntiːn/.

The number 17 has wide significance in pure mathematics Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions, as well as in applied sciences Fields of engineering are closely related to applied sciences. Applied science is important for technology development. Its use in industrial settings is usually referred to as research and development, law Law is a system of rules, usually enforced through a set of institutions. Laws can shape or reflect politics, economics and society in numerous ways and serves as a primary social mediator of relations between people. Contract law regulates everything from buying a bus ticket to trading on derivatives markets. Property law defines rights and, music Music is an art form whose medium is sound. Common elements of music are pitch , rhythm (and its associated concepts tempo, meter, and articulation), dynamics, and the sonic qualities of timbre and texture. The word derives from Greek μουσική (mousike), "(art) of the Muses.", religion Religion is the belief in and worship of a god or gods, or in general a set of beliefs explaining the existence of and giving meaning to the universe, usually involving devotional and ritual observances, and often containing a moral code governing the conduct of human affairs, sports A sport is commonly defined as an organized, competitive, and skillful physical activity requiring commitment and fair play.[note] It is governed by a set of rules or customs. In a sport the key factors are the physical capabilities and skills of the competitor when determining the outcome . The physical activity involves the movement of people,, and other cultural phenomena Popular culture is the totality of ideas, perspectives, attitudes, memes, images and other phenomena that are deemed preferred per an informal consensus within the mainstream of a given culture, specifically Western culture of the early to mid 20th century and the emerging global mainstream of the late 20th and early 21st century. Heavily.

Look up seventeen in Wiktionary Wiktionary is a multilingual, web-based project to create a free content dictionary, available in over 151 languages. Unlike standard dictionaries, it is written collaboratively by volunteers, dubbed "Wiktionarians", using wiki software, allowing articles to be changed by almost anyone with access to the website, the free dictionary.

Contents

In mathematics

Seventeen is the 7th prime number In mathematics, a prime number is a natural number that has exactly two distinct natural number divisors: 1 and itself. The smallest twenty-five prime numbers (all the prime numbers under 100) are:. The next prime is nineteen 19 is the natural number following 18 and preceding 20. It is a prime number, with which it forms a twin prime A twin prime is a prime number that differs from another prime number by two. Except for the pair , this is the smallest possible difference between two primes. Some examples of twin prime pairs are (3, 5), (5, 7), (11, 13), (17, 19), (29, 31), (41, 43), and (skipping quite a few), (821, 823). Sometimes the term twin prime is used for a pair of. 17 is the sum of the first four primes. 17 is the sixth Mersenne prime exponent, yielding 131071. 17 is an Eisenstein prime with no imaginary part and real part of the form 3n − 1.

17 is the third Fermat prime, as it is of the form 23 + 1, and it is also a Proth prime. Since 17 is a Fermat prime, heptadecagons The regular heptadecagon is a constructible polygon, as was shown by Carl Friedrich Gauss in 1796 can be drawn with compass A compass is a navigational instrument for determining direction relative to the Earth's magnetic poles. It consists of a magnetized pointer free to align itself with Earth's magnetic field. The compass greatly improved the safety and efficiency of travel, especially ocean travel. A compass can be used to calculate heading, used with a sextant to and ruler A ruler, sometimes called a rule or line gauge, is an instrument used in geometry, technical drawing, printing and engineering/building to measure distances and/or to rule straight lines. Strictly speaking, the ruler is essentially a straightedge used to rule lines[citation needed] and the calibrated instrument used for determining measurement is. This was proven by Carl Friedrich Gauss Johann Carl Friedrich Gauss (pronounced /ˈɡaʊs/; German: Gauß listen , Latin: Carolus Fridericus Gauss) (30 April 1777 – 23 February 1855) was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy.[1] Another consequence of 17 being a Fermat prime is that it is not a Higgs prime for squares or cubes; in fact, it is the smallest prime not to be a Higgs prime for squares, and the smallest not to be a Higgs prime for cubes.

17 is the only positive Genocchi number that is prime, the only negative one being −3. It is also the third Stern prime.

As 17 is the least prime factor of the first twelve terms of the Euclid–Mullin sequence, it is the thirteenth term.

Seventeen is the aliquot sum of two numbers, the odd discrete semiprimes 39 and 55 Year 55 was a common year starting on Wednesday (link will display the full calendar) of the Julian calendar is the base of the 17-aliquot tree.

There are exactly seventeen two-dimensional space (plane symmetry) groups In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines any two of its elements to form a third element. To qualify as a group, the set and the operation must satisfy a few conditions called group axioms, namely closure, associativity, identity and invertibility. While these are familiar from. These are sometimes called wallpaper groups A wallpaper group is a mathematical classification of a two-dimensional repetitive pattern, based on the symmetries in the pattern. Such patterns occur frequently in architecture and decorative art. There are 17 possible distinct groups, as they represent the seventeen possible symmetry types that can be used for wallpaper Wallpaper is a kind of material used to cover and decorate the interior walls of homes, offices, and other buildings; it is one aspect of interior decoration. It is usually sold in rolls and are put onto a wall using wallpaper paste. Wallpapers can come either plain , or with patterned graphics.

Like 41, the number 17 is a prime that yields primes in the polynomial In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative, whole-number exponents. For example, x2 − 4x + 7 is a polynomial, but x2 − 4/x + 7x3/2 is not, because its second term involves division by the variable x n2 + n + p, for all positive n < p − 1.

In the Irregularity of distributions problem, consider a sequence of real numbers In mathematics, the real numbers include both rational numbers, such as 42 and −23/129, and irrational numbers, such as pi and the square root of two; or, a real number can be given by an infinite decimal representation, such as 2.4871773339..., where the digits continue in some way; or, the real numbers may be thought of as points on an between 0 and 1 1 is a number, numeral, and the name of the glyph representing that number. It represents a single entity, the unit of counting or measurement. For example, a line segment of "unit length" is a line segment of length 1 such that the first two lie in different halves of this interval In mathematics, a interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set. For example, the set of all numbers x satisfying is an interval which contains 0 and 1, as well as all numbers between them. Other examples of intervals are the set of all real numbers , the, the first three in different thirds, and so forth. The maximum possible length of such a sequence is 17 (Berlekamp & Graham, 1970, example 63).

Either 16 or 18 unit squares can be formed into rectangles with perimeter equal to the area; and there are no other natural numbers In mathematics, there are two conventions for the set of natural numbers: it is either the set of positive integers {1, 2, 3, ...} according to the traditional definition; or the set of non-negative integers {0, 1, 2, ...} according to a definition first appearing in the nineteenth century with this property. The Platonists Platonism is the philosophy of Plato or the name of other philosophical systems considered closely derived from it. In a narrower sense the term might indicate the doctrine of Platonic realism. The central concept of Platonism is the Theory of Forms: the transcendent, perfect archetypes, of which objects in the everyday world are imperfect copies regarded this as a sign of their peculiar propriety; and Plutarch Plutarch, born Plutarchos then, on his becoming a Roman citizen, Lucius Mestrius Plutarchus (Μέστριος Πλούταρχος), c. 46 – 120 AD, was a Greek historian, biographer, essayist, and Middle Platonist known primarily for his Parallel Lives and Moralia. He was born to a prominent family in Chaeronea, Boeotia, a town about twenty notes it when writing that the Pythagoreans Pythagoreanism is a term used for the esoteric and metaphysical beliefs held by Pythagoras and his followers, the Pythagoreans, who were considerably influenced by mathematics. Pythagoreanism greatly influenced Platonism. Later revivals of Pythagorean doctrines led to what is now called Neopythagoreanism "utterly abominate" 17, which "bars them off from each other and disjoins them".[2]

17 is the tenth Perrin number, preceded in the sequence by 7, 10, 12.

In base 9, the smallest prime with a composite sum of digits is 17.

17 is known as the Feller number, after the famous mathematician William Feller William Feller born Vilibald Srećko Feller (July 7, 1906 – January 14, 1970), was a Croatian-American mathematician specializing in probability theory who taught at Princeton University Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution for many years. Feller would say, when discussing an unsolved mathematical problem, that if it could be proved for the case n = 17 then it could be proved for all positive integers n. He would also say in lectures, "Let's try this for an arbitrary value of n, say n = 17."

Similar to Feller, Prof. Vadim Khayms of Stanford University is also known to use 17 as an arbitrary value during lectures. His Computational Mathematics for Engineers course includes 17 lectures.

17 is the least random number[3], according to the Hackers Today, mainstream usage mostly refers to computer criminals, due to the mass media usage of the word since the 1980s. This includes script kiddies, people breaking into computers using programs written by others, with very little knowledge about the way they work. This usage has become so predominant that a large segment of the general public is' Jargon File The Jargon File is a glossary of hacker slang. The original Jargon File was a collection of hacker slang from technical cultures such as the MIT AI Lab, the Stanford AI Lab , and others of the old ARPANET AI/LISP/PDP-10 communities, including Bolt, Beranek and Newman, Carnegie Mellon University, and Worcester Polytechnic Institute. There is a proven theorem that 17 is the value most likely to be picked as a "random Randomness is a concept of non-order or non-coherence in a sequence of symbols or steps, such that there is no intelligible pattern or combination. Randomness has somewhat disparate meanings as used in several different fields. It also has common meanings which may have loose connections with some of those more definite meanings. The Oxford" number when such is needed in journalism which is derived from the Feller number.[4]

It is a repunit prime in hexadecimal In mathematics and computer science, hexadecimal is a positional numeral system with a radix, or base, of 16. It uses sixteen distinct symbols, most often the symbols 0–9 to represent values zero to nine, and A, B, C, D, E, F (or alternatively a through f) to represent values ten to fifteen. For example, the hexadecimal number 2AF3 is equal, in (11).

It is believed that the minimum possible number of givens for a sudoku Sudoku (数独, sūdoku?, listen ) (English pronunciation: /suːˈdoʊkuː/ soo-DOH-koo) is a logic-based, combinatorial number-placement puzzle. The objective is to fill a 9×9 grid with digits so that each column, each row, and each of the nine 3×3 sub-grids that compose the grid (also called "boxes", "blocks", "regions& puzzle with a unique solution is 17, but this has yet to be proven.

There are 17 orthogonal curvilinear coordinate systems In mathematics and its applications, a coordinate system is a system for assigning an n-tuple of numbers, scalars or variables to each point in an n-dimensional space. This concept is part of the theory of manifolds. "Scalars" in many cases means real numbers, but, depending on context, can mean complex numbers or elements of some other (to within a conformal symmetry) in which the 3-variable Laplace equation can be solved using the separation of variables In mathematics, separation of variables is any of several methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs on a different side of the equation technique.

17 is the first number that can be written as the sum of a positive cube and a positive square in two different ways; that is, the smallest n such that x3 + y2 = n has two different solutions for x and y positive integers. The next such number is 65.

In science

Age 17

In culture

Music

Film

Print

Religion

In sports

In other fields

Seventeen is:

Historical years

A.D. 17, 17 B.C., 1917, 2017, etc.

References

  1. ^ John H. Conway and Richard K. Guy, The Book of Numbers. New York: Copernicus (1996): 11. "Carl Friedrich Gauss (1777–1855) showed that two regular "heptadecagons" (17-sided polygon) could be constructed with ruler and compasses."
  2. ^ Babbitt, Frank Cole (1936). Plutarch's Moralia. V. Loeb. http://penelope.uchicago.edu/Thayer/E/Roman/Texts/Plutarch/Moralia/Isis_and_Osiris*/C.html#42
  3. ^ "Random numbers"
  4. ^ Language Log: Another trip down Random Rd
  5. ^ For example, the patriarch Jacob lived 17 years years after his son Joseph went missing and presumed dead, and lived 17 years after their reunion in Egypt, and the lifespans of Abraham aged 175, Isaac aged 180, and Jacob aged 147 are not a coincidence. "(The sum of the factors in all three cases is 17; of what possible significance this is, I have no idea.)" Leon Kass, The beginning of wisdom: reading Genesis,(Simon and Schuster, 2003), ISBN 9780743242998, p. 413 n. 10 (citing Genesis 47:28), quote from p. 629 n. 18, found at Google Books. Retrieved June 17, 2009.
  6. ^ http://scienceblogs.com/cognitivedaily/2007/02/is_17_the_most_random_number.php
  7. ^ http://blogs.discovermagazine.com/cosmicvariance/2007/01/30/the-power-of-17/

External links

Categories: Integers

 

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Schleck wins 17th stage but Contador set for title - The Associated Press
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Grand Finale The famous PTCA raffle

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the school of Mary: Homily 17th Sun O.T. Year C: How to Pray
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the school of Mary: Homily 17th Sun O.T. Year C: How to Pray

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Homily . 17th. Sun O.T. Year C: How to Pray. Why is it that of all the things that are the most life-giving in our faith, prayer can be the most confounding? The questions that we have when we first learn to pray continue to pop-up when ...

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How many students are in the circle if the 2nd student is directly across from the 17th?
Q. How many students are in the circle if the 2nd student is directly across from the 17th?
Asked by vanessa a - Wed Oct 7 22:25:17 2009 - - 2 Answers - 0 Comments

A. 30,..The way to think about this is to realize that student # 1 is sitting accross from student # 16,..so studnt # 15 must be sitting across from # 30,.who must be sitting to the left of # 1,..Another way to figure it out, is to just count on your fingers,..
Answered by tecopa jack - Thu Oct 8 05:37:02 2009

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